I have major concerns about the safety of the doppler, so for my last two pregnancies we used only a fetoscope. By the way, I didn't start to feel movement until quite late in my last pregnancy -- around 20 weeks -- so I couldn't rely on that to tell me the baby was okay. I just figured, what will be will be, and if the pregnancy turns out not to be viable, I can't do anything about it anyway, so why worry about it? I also liked the idea of allowing my connection to the baby to happen naturally, on nature's timetable.
ETA: I forgot to answer your other question. I did have a fetoscope and used it mainly to help determine position, because although I know that breech is a normal variation, I still have some fear surrounding it. If I knew the baby was vertex I wouldn't have to work through that fear. Kind of a laziness on my part I guess.
I never had a problem hearing the heartbeat, although sometimes it was faint due to baby's position. Also, sometimes the baby can "hide" behind the placenta, but mine was conveniently to the side rather than in front.
We didn't check FHTs in labor. I felt very certain that all was right -- mostly intuition (which can be very powerful if the mother is in a situation where can access and pay attention to it,) but also I had some idea of what normal labor should look like for me, under ideal conditions.